In designing an imaging system, it is important to be able to determine the magnitude of the level of image degradation to be expected in the final image as viewed by the observer. Understanding the magnitude of the image degradations due to grain is also important to the use of the image reproduction system and can have a major impact on the selection of key elements for use in the imaging chain.
In an imaging system, the variations in otherwise uniform responses to exposing light are referred to as noise. In a traditional photographic system, these variations in the density can be observed through physical measurement by measuring the optical density of photographic materials, such as film or paper, with a microdensitometer. The root mean square (rms) value or standard deviation is used as a measure of the variation in density of an otherwise uniform area. This value is referred to as the granularity. An output image is perceived by an observer and the perception of these unwanted, random fluctuations in optical density are called graininess or noise appearance. Thus, the physically measured quantity of granularity is perceived by the observer as a level of graininess.
Various efforts have been made to estimate and quantify the appearance of noise, or graininess, in an output image. C. Bartleson, in “Predicting Graininess from Granularity,” J. Phot. Sci., Vol. 33, No. 4, pp. 117–126, 1985, showed that graininess is dependent upon the granularity at a visual print density of 0.8. He determined the following relationship between the graininess Gi and the granularity σv Gi=a*log(σv)+b where a and b are constants.
Bartleson's work made it possible to estimate the graininess that a given imaging system will produce. Unfortunately, the graininess of different images produced from a common imaging system can have a huge variation. This is because any image transform that is applied to create the output image can alter the visibility of noise in a system. For example, a photographic negative can be imaged with an enlarger onto photographic paper. However, the noise appearance of the output print is highly dependent on the exposure given to the negative. Thus, the noise appearance of any given output image produced with a given imaging system may be quite different than the estimate enabled by Bartleson's work.
In U.S. Pat. No. 5,641,596 issued Jun. 24, 1997, Gray et al. describe a method of determining a noise table. Noise tables describe the density dependent noise of a particular image capture device, and therefore quantify the density dependent noise of images created by the image capture device. The noise table is usually modeled as the output from a specific scanning device and image capture device (such as film.) Alternatively the noise table could represent a digital image capture, or photographic film. A noise table represents the standard deviation of noise as a function of mean code value. However, a noise table alone is not a good indicator of the visibility of noise in an output image. An imaging system's output image is a product of multiple image transforms, each of which modifies its noise characteristics. Therefore, a pre-output noise table (such as a noise table quantifying the characteristics of an image capture device) does not represent the noise characteristics of an output image.
Noise information has been used to modify parameters of a user-selected algorithm. Cottrell et al., in U.S. Pat. No. 5,694,484 issued Dec. 2, 1997, describe a method of using characteristic information (e.g. Modulation Transfer Function and Wiener Power Spectrum to characterize noise) of input and output devices, calculating an objective metric of image quality, and determining the parameters for an image transform (such as sharpening boost) by optimizing the objective metric of image quality. Cottrell et al. again make the implicit assumption that all output images produced by a common imaging system will have a similar appearance of noise. However, this is not the case. While the images produced directly from an imaging device may have similar noise and sharpness characteristics, these characteristics may be vastly modified by the image transforms that produce the output image. In addition, for many imaging systems, for example, U.S. Pat. Nos. 6,097,470 and 6,097,471 both issued Aug. 1, 2000 to Buhr et al., the operation of image transforms vary based on an analysis of the image. The effect of image dependent image transforms is not considered by Cottrell.
Keyes et al. in U.S. Pat. No. 6,091,861, issued Jul. 18, 2000, describe a method of determining a sharpening parameter based on the exposure (i.e. the SBA balance) of the image. Their method also takes into account the granularity of the image and computes an expected graininess value (PGI), which is related to the granularity. However, this method does not have the flexibility to take into account the effects of the application of an image dependent image transform. Additionally, summarizing the noise on the print by using the exposure is prone to error, since even an image with a normally exposed subject can easily contain background areas that contain noise of a vastly different magnitude.
Another method of determining the noise appearance in a particular output image is to compare that output image to a set of standard noise examples arranged in a ruler. The first grain slide or ruler was designed and fabricated by Thomas Maier et al. See for example, T. O. Maier and D. R. Miller, “The Relationship Between Graininess and Granularity” SPSE's 43 Annual Conference Proceedings, SPSE, Springfield, Va., 1990, pp. 207–208. C. James Bartleson determined the fundamental relationship relating the granularity and graininess.
Maier et al. produced a series of uniform neutral patches of grain at the same average density with increasing amounts of grain using a digital simulation instrument. They then used microdensitometer measurements and the fundamental psychophysical relationship to relate the graininess to the rms granularity. Cookingham et al. produced improved grain rulers as described in U.S. Pat. Nos. 5,709,972 issued Jan. 20, 1998, and 5,629,769 issued May 13, 1997. While such noise rulers do effectively allow for an individual to numerically quantify the appearance of noise in an output image, the process is labor intensive and requires a human observer to individually evaluate each output image.
Therefore, there exists a need for an improved noise metric that avoids the problems noted above.